Question

Two coherent monochromatic light beams of intensities 4I and 9I are superposed. The maximum and minimum possible intensities in the resulting beam are

• A. 4I and 9I
• B. 16I and 21I
• C. 2I and 3I
• D. 25I and I

Hint:

In the case of interference of coherent waves, the maximum intensity is the sum of the individual intensities plus twice the square root of their product, while the minimum intensity is the difference.

Answer 1

The Correct Option is D

Step 1: Understanding the intensity formula for superposition.
When two coherent light waves interfere, the resultant intensity is determined by the superposition of their electric fields. The maximum intensity \( I_{\text{max}} \) and minimum intensity \( I_{\text{min}} \) are given by the following formulas: \[ I_{\text{max}} = I_1 + I_2 + 2 \sqrt{I_1 I_2} \] \[ I_{\text{min}} = I_1 + I_2 - 2 \sqrt{I_1 I_2} \] where \( I_1 \) and \( I_2 \) are the intensities of the two waves. Step 2: Apply the given intensities.
Let \( I_1 = 4I \) and \( I_2 = 9I \). Using the formulas: \[ I_{\text{max}} = 4I + 9I + 2 \sqrt{4I \times 9I} = 13I + 6I = 25I \] \[ I_{\text{min}} = 4I + 9I - 2 \sqrt{4I \times 9I} = 13I - 6I = I \] Step 3: Conclusion.
Thus, the maximum and minimum possible intensities are \( 25I \) and \( I \), which corresponds to option (D).